WASHINGTON, March 3 (Reuters) - U.S. lawmakers are considering options such as imposing sanctions on Russia's banks and freezing assets of Russian public institutions and private investors because of Moscow's moves in Ukraine, U.S. Senator Chris Murphy, the chairman of the Senate's Europe subcommittee, said on Monday.

However, U.S. sanctions against Russia will have little effect if they are not matched by actions from Europe, Murphy said in a telephone interview.

"Unilateral U.S. sanctions against Russia are not going to have much an effect if Europe remains a haven for Russian banks and Russian oligarchs to stash and invest their money," the Connecticut Democrat said.

"If the United States shuts its economic doors to Russia and Europe leaves its doors open, there won't be much change in behavior from Moscow," he said.

U.S. lawmakers have been in discussions about what legislative support they can give President Barack Obama's administration as it determines how to react to Moscow's military action in neighboring Ukraine.

The United States has the ability to sanction large Russian banks, which are controlled by the government, to freeze the assets in the United States of both Russian public institutions as well as their largest private institutional investors and to impose travel bans, Murphy said.

Americans are strongly opposed to military intervention but several lawmakers support sending international observers into southern and eastern Ukraine, as well as economic sanctions and travel restrictions on Russians involved in Ukraine.

"I don't think that the Russian industrial community wants to return to the Cold War when they couldn't move their money and they couldn't travel," Murphy said.

Russia paid a financial price on Monday for its military intervention in neighboring Ukraine, with stocks, bonds and the rouble plunging as President Vladimir Putin's forces tightened their grip on the Russian-speaking Crimea region.

U.S. lawmakers also are considering ways to support the new government in Kiev. At the Obama administration's request, members of both the Senate and House of Representatives are working on legislation to support U.S. loan guarantees for Ukraine, congressional aides said. (Reporting by Patricia Zengerle; Editing by Bill Trott)